article
Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure
published
yes
Peter
Reimann
author 70631
29105470
department
Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator rho of low purity, tr rho(2) << 1, and yielding the ensemble averaged expectation value tr(rho A) for any observable A. Assuming that the given statistical ensemble rho is generated by randomly sampling pure states vertical bar psi > according to the corresponding so-called Gaussian adjusted projected measure (Goldstein et al. in J. Stat. Phys. 125:1197, 2006), the expectation value <psi vertical bar A vertical bar psi > is shown to be extremely close to the ensemble average tr(rho A) for the overwhelming majority of pure states vertical bar psi > and any experimentally realistic observable A. In particular, such a 'typicality' property holds whenever the Hilbert space H of the system contains a high dimensional subspace H+ subset of H with the property that all vertical bar psi > epsilon H+ are realized with equal probability and all other vertical bar psi > epsilon H are excluded.
SPRINGER2008
eng
measuresGaussianquantum statistical mechanicsmicrocanonical density matricesquantum ensemble theory
JOURNAL OF STATISTICAL PHYSICS
0022-4715
1572-9613
00025853990000810.1007/s10955-008-9576-1
1325921-935
Reimann P (2008) <br />Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure.<br />JOURNAL OF STATISTICAL PHYSICS 132(5): 921-935.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Reimann, P. (2008). Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. <em>JOURNAL OF STATISTICAL PHYSICS</em>, <em>132</em>(5), 921-935. doi:10.1007/s10955-008-9576-1</div>
Reimann, P. (2008): Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure <em>JOURNAL OF STATISTICAL PHYSICS</em>,132:(5): 921-935.
Reimann, P. (2008). Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. <em>JOURNAL OF STATISTICAL PHYSICS</em> 132, 921-935.
Reimann, Peter. “Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure”. <em>JOURNAL OF STATISTICAL PHYSICS</em> 132.5 (2008): 921-935.
P. Reimann, Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure, JOURNAL OF STATISTICAL PHYSICS <strong>132</strong>, 921 (2008).
P. Reimann, “Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure”, <em>JOURNAL OF STATISTICAL PHYSICS</em>, vol. 132, 2008, pp. 921-935.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Reimann, Peter. 2008. “Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure”. <em>JOURNAL OF STATISTICAL PHYSICS</em> 132 (5): 921-935.</div>
Reimann P (2008) <br /><em>JOURNAL OF STATISTICAL PHYSICS</em> 132(5): 921-935.
Reimann, P. (2008). Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. <em>JOURNAL OF STATISTICAL PHYSICS</em>, <em>132</em>(5), 921-935. doi:10.1007/s10955-008-9576-1
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Reimann, P. (2008). Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. <em>JOURNAL OF STATISTICAL PHYSICS</em>, <em>132</em>(5), 921-935. SPRINGER. doi:10.1007/s10955-008-9576-1.</div>
P. Reimann, “Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure”, <em>JOURNAL OF STATISTICAL PHYSICS</em>, <strong>2008</strong>, <em>132</em>, 921-935.
Reimann, P., 2008. Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. <em>JOURNAL OF STATISTICAL PHYSICS</em>, 132(5), p 921-935.
Reimann, P.: Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. JOURNAL OF STATISTICAL PHYSICS. 132, 921-935 (2008).
Reimann P. Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. <em>JOURNAL OF STATISTICAL PHYSICS</em>. 2008;132(5):921-935.
15866262010-04-26T09:43:38Z2018-07-24T12:58:38Z